There are only a finite number of positive integers that reach 1, the largest being
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written in base ten, or
16305135035545012466241561026121103363306322322236102306112633635125110360151360300311453551142635324265123415554443332454022032233040544430302554231060412532131112116345613044565322211534161103334664051630552566011014222051234236045203546536102314012235205531252342040061531632412331533551053220253051042420303303631113423100254556460110245204303334064650116505101360330566353412030645146104452415500005624356214333051641130221406221044403240542552550505000615400036613432030451361156030555203112252452566623660115010134004236130161116132166222266226525103166320522165254423325655645022643554552444261054126542565444003545532543131430214300146534156632045511116226643015040424200211165641135432555523132040423340361361151660303666221621641554602134622206442464365446230411454064025141603105322622062410351152226562234402256363212225353600253032644551452536354666531145423132120154251652151531035660054000344162665655205203464635155112221451231233510460456454045245225442350165611065531445253504645431014210445143660632044225663663613002061512035436665010435233041360015423663245553425445264154343260346013522530416265146330236445646253312653456001242113424553465066662663360210036605406120006644633462201306442453434563333426630660123245140446642320125055454055205216225264013113020024053650405331523360515525452041456643161044323501532210305633461010214244520134636262461232065614560246605663006204514633201615401310252665561356346563152446235101525043256033626226401005651615343204154204135546015566024331521405205320064010613016336355641252104243110316664356364111662226114420012341400636011445610650464554625136262421230454436150265062454201533221003156643411256403401425020611310446630150003461316202253163462506023021252254122151121605441222260521261245111245413155615361535215644003010343454611600331530102134561441442543140603140450423612620301461200145214126143646033154553550520625211423441662420653621551436266335430160062102511153653365232105246354222311164030461512625556605366441135604333502641444524140126654025134425435061226064064605166224263502302614463232534451240113360413352302522113621011454612006020014364360526331254611540644532524042004502264055633530600503134236213460332252662222204415132665436264351331556516455445631031422323620650052404350535610035060320111166016240001203045021465232226616663221424155131314051601010551663063421233145214334560426041235302363123531402134466603152553330302052565443402435262354655223003164011533034635305240660454516622410633653453355422450623403415452166303145010623346223561023003304564403346462362352331231645620450360054216601156363615240245116545553503122150053052632163001601322156145316551653302334113562362534345352342321302623354362443000003606465341151244263322430210452041360422365116202153356162506211236365102162450642104253354011211331351303316636244654253226261260633641332414604545416036215664522611133412202160161003351040616143211531111122005102620333453233164461122233446205306415562644562165431165565036626150204363603662303460000225352050505016136466042545563461310306536335061524124304643502022555643015540665423612206324450430306442065120341653310226564043311146202052205246060465204264026063224054003421155536231024545435221603152454605214346466451530004006505456200026413612210601161504620303600061302210414234632633452426513036051553042256314243660441462505033065153035626062556113563264661136351046056443365200403415404234603413262540125360046306012360312102322206236346304025530654511560255653154420430426365255221233141325430456632553644636151363403605132131143640323635215556405646222122166502331532511556103663414063435110325554101304421240134646151411234116556513002332622303410066534312124514616060251063244646266131510314132606020663221362552533245646242160254135104564214356545510613430561035264665130663506153152240222403536251563255665323010125134232351444610440256232350433113332614662236035555104320663263550654262404266211540531025031105305626233622326015640225412230556453043212654335006614306610401205022330042312624465643441306146220153602523013323361513066030544364350220614116662064261616260334466214103233542036105203463603514551646361235012141363245132414141042004450520536160550150122605565115514306152446316115516331034300555063523331045305505163044363361114261462405506666515625134240005621016251015120111562141253663415325442065041313636421363643561126261142526166315664063340466232311025245435066033162456234405062030650112643154422526651254311332555402520226053206121252300614254604232124056556625220051142214045263213216316310430013246064460215136214445114563343050423644262624506124261403552015331104600545100011135455112152325162461346004160023363550050011465240650426245220565310536343126643215365523342220654315322125463610554222636522131346621221066102622565565302413201503304345411361035531365311555010300550360653243360504016226045360043311324164640412650041230462510120230366165505135634141233133400045230332415336662120214055355541345505640521053310330635016046403524621162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written in base seven.
This number takes 2046 steps to reach 1. I have plotted the count of positive integers (out of a total 693633 available) that take n steps (from n = 0 to n = 2046) to get to 1 in a graph. The smaller, darker-blue plot at the bottom-left is the count of positive integers (out of a total 15095 available) that take n steps (from n = 0 to n = 440) to get to 1 in the base-10 version of the procedure.
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